Wednesday, November 14, 2012

On its own, a random number generator is not fair, moral, or kind. It is just random.

Which is probably why RNG makes for such terrible gameplay.

Much of GW2's endgame* focuses on the hunt for cosmetic improvements - legendary items with no stat bonus, but unique skins / animations. To keep these items rare, the precursor weapons to legendary items are low-chance results from mystic forge gambling.

But before the system is thrown into the dustbin of poor implementation, I wanted to take a moment and examine one reason why using RNG to gate progression is a terrible idea: the distribution of cost.

Luck and Cost
Some players get a precursor on their attempt... while others throw thousands of items into the forge with no result. I want to visualize that difference.

From the last post, I have a reasonable expectation that four rare items have a 20% chance of returning an exotic. I'm going to guess that this exotic has either a 1%, 1.3%, 2% or 4% chance of being a precursor. And I'll check three different ways of getting precursors:

Plan 1: crafting rares, selling all exotic outcomes until a precursor is found

Plan 2: crafting rares, reforging all non-precursor exotics

Plan 3: crafting exotics, reforging all non-precursor exotics

Under these conditions, here is the estimated (average) cost of mystic forge gambling (in gold), using greatswords as a baseline, broken down the the chance for an exotic to be the precursor.**

These averages are (generally) reasonable. Under these assumptions, even at a 1% chance, a precursor is around a 200g investment, making it expensive, but attainable.

There are two things to note.

Crafting exotics to obtain a precursor is three times as expensive as crafting rares. This doesn't necessarily mean that using exotics to obtain precursors is a bad idea. They might have 3x the chance of yielding precursors - its just that nobody has the data to find out. Fortunately, in terms of puzzling out why luck is a bad way to gate progression, this doesn't matter, so I'll focus on plan 1 & 2 from this point on.

Given the current price of precursors... either the precursors are much rarer than I've assumed, or using the mystic forge may be profitable even at current prices.***

Luck and Extreme Outcomes

Average cost isn't the issue. Its the distribution of cost that is the problem.

And that is where luck hurts players.

Here, I've simulated the results of 5000 players using plan 1 to obtain a precursor from the mystic forge, varying the chance that an exotic is a precursor. I've plotted how much the luckiest 10% of players pay for a precursor by gambling, the unluckiest 10%, and two measures of the average player (mean and median).

As precursors become harder to obtain (moving to the left), the average cost of creating a precursor for the unluckiest 10% of players grows exponentially. For example, if an exotic has a 1% chance to be a precursor from the mystic forge, the unluckiest 10% spend an average of just over 800 gold to get a precursor, compared to around 200g for the average player.

And that is the problem with RNG: extreme outcomes.

Extremes are great if you're lucky, but horrible for the person throwing gold away.

A simple fix would be to institute a progressively increasing drop chance once a threshold has been exceeded. Great way to fix the discouraging luck issue.

The problem with RNG is that players don't earn the item. Which cheapens it. And it cheapens the journey. Because there is no journey, just a slot machine. Imagine Arthur winning Excalibur at a casino. Not epic.

* Stuff-to-do at 80.
** The choice of greatswords here doesn't shape the cost much - while the TP cost of precursors varies wildly, most weapons have approximately the same crafting cost. I'm also assuming that exotics are sold to market in Plan 1 for 1g.
*** Of course, if they're rarer, then some of the cheaper precursors are tremendous losses.

Tuesday, November 13, 2012

As it turns out, the mystic forge is actually the genie Zommoros. Strange new lifeform? Time for the asura to get investigating.*

The mystic forge serves three purposes:

Crafting via recipes. Placing specific combinations of items into the forge will yield a guaranteed result. This includes mystic weapons, some of the coolest exoticskins in-game, and legendaries. Unfortunately, Zommoros doesn't list recipes for the forge. They have to be discovered / looked-up on third-party websites (the wiki).

Upgrades of materials. Common, fine, and rare crafting materials can be promoted into a smaller number of higher tier materials [source].

Gambling. Placing four items into the mystic forge (of the same quality) will give one higher-level item, with chance to improve its rarity.

Fortunately, developer posts have noted that the mystic forge isn't affected by either diminishing returns or magic find. This makes examining these mechanics considerably easier.

I fed 2400 weapons into Zommoros to test out gambling, he gave me the data here.

Level Up!

Placing four items into the mystic forge will yield a higher-level item. How many levels higher?

On average**, the resulting items were 7 levels higher than the input items.

The forge seems to use average item level for determining upgrades. Four same-level (even identical items) had the same average level upgrade as four items of various levels, but the same average item level.

The pattern is the same regardless of input item rarity or level (usual stats-nerds tests applied).

While four greens have an approximately 20% chance of yielding yellows, four blues have a 33% chance of yielding a green. (Usual stat nerd tests applied.) While they're included in the plot, since there are no yellow weapons below level 30, green weapons below level 20 have no observed chance of becoming yellow-quality weapons. I therefore excluded them from this analysis.

Take the increased chance of upgrades from blues with a grain of salt. While it is exceptionally unlikely I observed this difference from chance alone, most sources list the 20% upgrade rate as gospel.

Note: the drop-off in level 70+ greens is simply because I didn't record much data there. (Its expensive!)

*Now 100% more ethical. Sorry Malomedies.
**Well, I should say, on median. I - very rarely - obtained dramatically higher level items (up to 50 levels higher than the inputs). I'm guessing these are bugs. The items have no vendor value, and are soulbound on acquire. It looks like the item level of the result was just miscoded. Therefore, I excluded these from the analysis. More data required =D.